Nvidia Opens the Recipe Behind Its IMO Gold-Medal Math System

Nvidia researchers have published a full account of the system that carried its Nemotron 3 Ultra model to a gold-medal score at the 2026 International Mathematical Olympiad, and released almost everything needed to rebuild it. The technical report appeared on arXiv on 9 September, accompanied by two post-trained model checkpoints, the training data, the inference pipeline, the proofs submitted to the competition and a new benchmark of 200 previously unpublished olympiad problems.

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The system scored 30 points out of 42, above the 29-point gold threshold, with all submitted proofs graded by official IMO graders. It earned full marks on problems 1, 2, 4 and 5 and one point each on problems 3 and 6. What makes the result notable is not only the score but the method: the pipeline operated entirely in natural language, with no formal proof assistant, no external tools and no internet access.

That is a deliberate contrast with the approach that produced earlier headline results in mathematical AI. Systems built around formal verification, which translate problems into machine-checkable language, reached silver-medal level at the IMO in 2024. The 2025 competition was the first at which natural-language models cleared the gold threshold. Nvidia's contribution is to show how far an open, reproducible version of that second approach can go.

A system, not a single model

The most important caveat in the report is that the 30 out of 42 is a system score. No single checkpoint earned it. The pipeline draws on three Nvidia Nemotron 3 Ultra checkpoints, a model family with 550 billion parameters of which 55 billion are active at a time. One is the general-availability base model. The other two are specialists post-trained by the researchers: one through supervised fine-tuning on a proof-focused corpus, the other through reinforcement learning. The two specialists are released under the OpenMDW-1.1 licence.

The inference design combines generation, verification and refinement. In the first search round, the system samples 384 candidate proofs per problem: 16 attempts from each of eight solution-strategy prompts, run across all three checkpoints. A verification panel made up of the two specialist checkpoints then scores every candidate. A proof advances only if all 16 independent judgments across the panel score it as correct. Candidates that survive are refined using the panel's written critiques, and the pool of proofs accumulates across rounds until one is unanimously accepted.

A separate high-compute stage then re-grades each finalist. Every checkpoint produces 16 IMO-style judgments on a 0-to-7 scale, for 48 judgments per finalist, and the highest mean score wins, with ties broken in favour of the shorter proof.

What the ablation studies show

The report's value lies in its ablations, the experiments that isolate which choices mattered. On a 30-problem development set, judged by an independent panel of three commercial models, the reinforcement-learning specialist was the best single-checkpoint pipeline end to end, earning 180 of a possible 210 jury points against 165 for the fine-tuned specialist and 162 for the base model. The fine-tuned checkpoint, by contrast, solved more problems in the first round, suggesting the two specialists contribute differently to the search.

Verification was the other decisive variable. On a 300-proof audit set, the combined RL-and-SFT panel cut the false-accept rate, the failure mode that ends the search on an invalid proof, to about 1.1 percent. The RL checkpoint judging alone produced a 12.4 percent false-accept rate, and the base model produced 31.6 percent. The researchers' conclusion is that the two selective specialists catch each other's errors under a unanimity rule, which matters more than raw generation quality.

The report is also candid about what did not help. More elaborate routing between checkpoints changed early search behaviour without improving final coverage, and aggressive filtering of candidate proofs discarded attempts that later led to correct solutions.

The compute bill

The competition run was expensive. All six submitted proofs were found within roughly 707 million generated tokens and 1,464 GB200 GPU-hours. Completing the rounds already in flight brought the full run to about 2.31 billion tokens and 4,800 GB200 GPU-hours. The researchers released the resource accounting alongside the code, which is unusual and useful: it lets other labs estimate what a competition-grade run costs before attempting one.

Deployment is not trivial either. Running the checkpoints requires roughly 1.5 terabytes of high-bandwidth memory, about a single node of eight B200 GPUs, and the release is self-hosted with no hosted API or price list.

Natural language versus formal verification

The choice to work without a formal prover is the most consequential design decision in the report. Formal methods, in which a proof is translated into a language such as Lean and checked by software, have a large advantage: a verified proof is correct by construction. They also carry a large cost. Translating a competition problem into formal language is slow and skill-intensive, and a system that can work only in that medium is of limited use to a mathematician who wants to pose a question in ordinary prose.

Natural-language systems trade certainty for reach. Their output reads like a human solution, which makes it easier to review and to publish, but it has to be judged by other means. Nvidia's answer is statistical: use multiple checkpoints as judges, require unanimity, and select among finalists with a large panel. The false-accept figures show why that machinery is necessary. A single model judging proofs accepted wrong answers far more often than the combined panel, and the failure mode is severe, because a search that believes an invalid proof is finished stops looking for a correct one.

The approach also has a verification gap that no amount of judging fully closes. A panel of language models can be wrong together, especially on a problem near the edge of what they can solve. The strongest evidence for the IMO result is therefore not the system's own confidence but the official graders who awarded the points. For research use, the distinction matters: a natural-language pipeline is a way to generate candidates and feedback, not a substitute for checking a result that an important decision depends on.

The open-model strategy

Releasing the checkpoints, data and code under a permissive licence is consistent with how Nvidia has positioned its Nemotron family, using open weights to seed demand for the hardware that runs them. The commercial logic is straightforward. A company that sells GPUs benefits when capable open models exist, because they lower the barrier to building on Nvidia's platform and give customers a reason to buy compute rather than rent it.

That strategy has a cost. Once the recipe is public, anyone with the hardware can reproduce or improve it, including labs that compete with Nvidia's customers. The researchers appear to have accepted the trade, betting that the reputational and ecosystem gains from an open, reproducible result outweigh the risk of handing competitors a template. Whether that bet pays off will depend less on the IMO score than on how many teams adopt the recipe and report what they find.

The benchmark may outlast the score

The most durable artifact may be Nemotron-IMO-Bench, a set of 200 olympiad-level problems split evenly across algebra, combinatorics, geometry and number theory, each with a human-curated reference proof. The problems were created with the mathematician Titu Andreescu and kept unpublished so they cannot appear in any training corpus. Contamination, the risk that a benchmark's questions leaked into a model's training data, has become a central problem for evaluating math and coding models, and a fresh, withheld problem set is exactly what the field has been short of.

Independent reproduction is the obvious next test. Every performance figure in the release comes from Nvidia's own report. The IMO score has the strongest provenance because it was graded under competition conditions, but no outside lab has yet run the recipe end to end and reported a score on the new benchmark. Until that happens, the result should be read as the honest account of one frontier-scale run rather than a settled capability claim.

Why it matters beyond the medal

The result lands in a week when AI and mathematics have rarely been more entangled. On 8 September, OpenAI said a swarm of roughly 10,000 agents had found a solution to a long-standing problem in the Navier-Stokes equations, a claim that is formally checked in Lean but not yet independently accepted by the Clay Mathematics Institute. Nvidia's work points in a different direction: not towards a single dramatic proof, but towards a reproducible pipeline that turns inference-time compute into mathematical output and then opens the whole apparatus for others to examine.

That transparency is the actual news. A gold-medal score is a headline; a released training recipe, a withheld benchmark and a detailed compute budget are tools other researchers can build on. If the recipe reproduces, this week's quiet release will look more consequential than the score that prompted it.